Application of Metastructures for Targeted Low-Frequency Vibration Suppression in Plates

Purpose We present an approach that combines finite element analysis and genetic algorithms to find the optimal configuration of local resonators created in the host structure to suppress their vibration in a target low-frequency range. Such local resonators are indeed metastructures that alter the wave propagation in the host structure, thereby attenuating their vibration. Methods To demonstrate the approach, we cutout zigzag resonators in a thin aluminium plate that is subjected to base-excitations. The thin plate and the zigzag cutouts are modelled using the finite element method, and the optimal location and optimal tip mass of the zigzag cutouts are obtained using genetic algorithms through iterative simulations. Two case studies are considered, and the fitness function used in the optimization problem is the plate’s root mean square of vibration in a specific low-frequency range. In the first case, the plate has two aligned zigzag cutouts. In this case, the objective is to find the optimal linear location and tip masses of the two zigzag cutouts. In the second case, the plate also has two zigzag cutouts, but their linear and transverse locations can vary along with the respective tip masses. The two optimal specimens are manufactured and tested experimentally. Results Numerical results were compared to experimental results which demonstrate that the proposed approach is reliable and can be used to tune the band gap of plates, thereby maximizing the vibration attenuation in the target frequency range. Conclusion Genetic algorithms can be used along with finite element analysis and zigzag cutouts to tune the band gap of plates subjected to base-excitations. The approach can be extended to plates/structures with other types of excitations and boundary conditions.Open Access funding was graciously provided by the Qatar National Library

Application of Metastructures for Targeted Low-Frequency Vibration Suppression in Plates

In this paper, we present an approach that combines finite element analysis and genetic algorithms to find the optimal configuration of local resonators created in the host structure to suppress their vibration in a target low-frequency range. Such local resonators are indeed metastructures that alter the wave propagation in the host structure, thereby attenuating its vibration. To demonstrate the approach, we cutout zigzag resonators in a thin aluminium plate to attenuate its vibration. The thin plate and the zigzag cutouts are modeled using the finite element method, and the optimal location and tip mass of the zigzag cutouts are obtained using genetic algorithms through iterative simulations. Two case studies are considered, and the fitness function used in the optimization problem is the plate’s root mean square of vibration in a specific low-frequency range. In the first case, the plate has two aligned zigzag cutouts. In this case, the objective is to find the optimal linear location and tip masses of the two zigzag cutouts. In the second case, the plate also has two zigzag cutouts, but their linear and transverse locations can vary along with the respective tip masses. The two optimal specimens are manufactured and tested experimentally. The results obtained demonstrate that the proposed approach is reliable and can be used to tune the band gap of plates, thereby maximizing the vibration attenuation in the target frequency range. All the code used in this paper will be openly available at Qatar University Institutional Repository.Qatar National Research Fund (a member of Qatar Foundation) provided financial support for this research via the National Priorities Research Program, project number NPRP-8-1568-2-666. The statements made herein are solely the authors’ responsibility, and they are not of the QNRF or Qatar University

Generalized spatial aliasing solution for the dispersion analysis of infinitely periodic multilayered composites using the finite element method

The finite element (FE) method offers an efficient framework to investigate the evolution of phononic crystals which possess materials or geometric nonlinearity subject to external loading. Despite its superior efficiency, the FE method suffers from spectral distortions in the dispersion analysis of waves perpendicular to the layers in infinitely periodic multilayered composites. In this study, the analytical dispersion relation for sagittal elastic waves is reformulated in a substantially concise form, and it is employed to reproduce spatial aliasing-induced spectral distortions in FE dispersion relations. Furthermore, through an anti-aliasing condition and the effective elastic modulus theory, an FE modeling general guideline is provided to overcome the observed spectral distortions in FE dispersion relations of infinitely periodic multilayered composites, and its validity is also demonstrated.Qatar National Research Fund through Grant No. NPRP8-1568-2-666. Shim acknowledges start-up funds from the University at Buffalo (UB), and he is grateful to the support of UB Center for Computational Research

Application of Metastructures for Targeted Low-Frequency Vibration Suppression in Plates

Purpose We present an approach that combines finite element analysis and genetic algorithms to find the optimal configuration of local resonators created in the host structure to suppress their vibration in a target low-frequency range. Such local resonators are indeed metastructures that alter the wave propagation in the host structure, thereby attenuating their vibration. Methods To demonstrate the approach, we cutout zigzag resonators in a thin aluminium plate that is subjected to base-excitations. The thin plate and the zigzag cutouts are modelled using the finite element method, and the optimal location and optimal tip mass of the zigzag cutouts are obtained using genetic algorithms through iterative simulations. Two case studies are considered, and the fitness function used in the optimization problem is the plate’s root mean square of vibration in a specific low-frequency range. In the first case, the plate has two aligned zigzag cutouts. In this case, the objective is to find the optimal linear location and tip masses of the two zigzag cutouts. In the second case, the plate also has two zigzag cutouts, but their linear and transverse locations can vary along with the respective tip masses. The two optimal specimens are manufactured and tested experimentally. Results Numerical results were compared to experimental results which demonstrate that the proposed approach is reliable and can be used to tune the band gap of plates, thereby maximizing the vibration attenuation in the target frequency range. Conclusion Genetic algorithms can be used along with finite element analysis and zigzag cutouts to tune the band gap of plates subjected to base-excitations. The approach can be extended to plates/structures with other types of excitations and boundary conditions.Other Information Published in: Journal of Vibration Engineering & Technologies License: https://creativecommons.org/licenses/by/4.0See article on publisher's website: http://dx.doi.org/10.1007/s42417-022-00614-9</p